On maximal resonance of polyomino graphs

A polyomino graph is a finite plane 2-connected bipartite graph every interior face of which is bounded by a regular square of side length one. Let k be a positive integer, a polyomino graph G is k-resonant if the deletion of any i ≤ k vertex-disjoint squares from G results in a graph either having perfect matchings or being empty. If graph G is k-resonant for any integer k ≥ 1, then it is called maximally resonant. All maximally resonant polyomino graphs are characterized in this work. As a result, the least integer k such that a k-resonant polyomino graph is maximally resonant is determined.     

Optical potential calculations for molecular collisions

The Feshbach optical formalism is applied to elastic, nonreactive atom-diatom scattering on a single potential energy surface. The optical potential depends on GQ, the resolvent of E-QHQ, where Q projects onto open as well as closed channels. A method for generating GQ is developed which goes beyond the free-space approximation by partitioning the radial part of the intermolecular separation into a set of intervals, on each of which the projected interaction QVQ is represented by a constant diagonal form. The resulting GQ is used in calculations on a model collinear system. The calculations are carried out with various approximations on the full nonlocal optical potential equation for Pψ Emphasis is placed on two of these, one of which is characterized by a local homogeneous equation for Pψ, and the other by a local inhomogeneous equation for Pψ.     

Conductance of nano-tube junctions and its scaling law

The conductance is calculated by Landauer’s formula with a simple tight binding model for junctions connecting two different metallic carbon nanotubes. These junctions are formed by a pair of disclinations, a 5-membered ring and a 7-membered ring, without dangling bonds. Conductances of about eight hundred kinds of junctions are obtained. The conductance is determined only by the ratio i/R where i is the distance between the two disclinations and R is the circumference of the thinner tube. When i/R ? 1, the conductance is found to be almost proportional to (i/R)^-3. Even when the Fermi energy is shifted by doping, an extended scaling law holds, so far as the channel number is kept two.     

Packing in honeycomb networks

Molecules arranging themselves into predictable patterns on silicon chips could lead to microprocessors with much smaller circuit elements. Mathematically, assembling in predictable patterns is equivalent to packing in graphs. An H-packing of a graph G is a set of vertex disjoint subgraphs of G, each of which is isomorphic to a fixed graph H. If H is the complete graph K ₂, the maximum H-packing problem becomes the familiar maximum matching problem. In this paper we give algorithms to find a perfect packing of HC(n) with P ₆ and K _1,3 when n is even and thus determines their packing numbers. Further we also study the packing of HC(n) with 1, 3-dimethyl cyclohexane.     

The compensation effect revisited

It is generally accepted that the compensation effect arises when a linear relation between InA andE is detected for a simple reaction taking place over different catalysts or for different reactions over one catalyst. For a perfect linear relation between InA andE representation of the reaction rate constant in an Arrhenius plot results in a series of straight lines which intersect in a single point. The importance is stressed of defining unambiguously what is meant by the compensation effect, and it is shown how the scatter in the values of InA is translated into Arrhenius plots.     

Stochastic theory of direct simulation Monte Carlo method

A treatment of direct simulation Monte Carlo method as a Markov process with a master equation is given and the corresponding master equation is derived. A hierarchy of equations for the reduced probability distributions is derived from the master equation. An equation similar to the Boltzmann equation for single particle probability distribution is derived using assumption of molecular chaos. It is shown that starting from an uncorrelated state, the system remains uncorrelated always in the limit N→∞, where N is the number of particles. Simple applications of the formalism to direct simulation money games are given as examples to the formalism. The formalism is applied to the direct simulation of homogenous gases. It is shown that appropriately normalized single particle probability distribution satisfies the Boltzmann equation for simple gases and Wang Chang–Uhlenbeck equation for a mixture of molecular gases. As a consequence of this development we derive Birds no time counter algorithm. We extend the analysis to the inhomogeneous gases and define a new direct simulation algorithm for this case. We show that single particle probability distribution satisfies the Boltzmann equation in our algorithm in the limit N→∞, V _k →0, Δt→0 where V _k is the volume of kth cell. We also show that our algorithm and Bird’s algorithm approach each other in the limit N _k →∞ where N _k is the number of particles in the volume V _k .     

Short diastereoselective synthesis of cis- and trans-hexahydropyrido[2,1-a]isoindole derivatives

A new and highly stereoselective access to 4,10b-trans or 4,10b-cis hexahydropyrido[2,1-a]isoindole derivatives is reported, both requiring an intramolecular Mannich-type reaction as key step. The cis diastereoisomer is obtained in three steps from a 2-alkyl benzaldehyde through the stereoselective formation of a 2,6-cis-disubstituted piperidine, while the trans stereomer is efficiently obtained, in a single step, if a 2-formyl benzoic acid is involved in the Mannich cyclization process.     

A versatile synthesis of 2-substituted 4-amino-1,2,4,5-tetrahydro-2-benzazepine-3-ones

A mild and general strategy for the synthesis of 2-substituted 4-amino-1,2,4,5-tetrahydro-2-benzazepine-3-ones is described. The seven-membered lactam is prepared by intramolecular amide bond formation from the intermediate amino acid, which is obtained either by reductive alkylation of a variety of amines with N-Boc,N-Me-ortho-formyl-Phe and Phth-ortho-formyl-Phe, or by reductive amination of a variety of aldehydes with N-Boc-ortho-aminomethyl-Phe.     

La methode polarovoltrique : Principes généraux et bases de la méthode

The various steps in the development of the polarovoltric method and its utilisation in an automatic titration apparatus employing 2 polarized platinum electrodes are described. The method is based on the use of 2 types of polarization relationships applied to different chemical systems. These relationships are of the type I = f(V) and V = f(U), where V is the potential measured at the electrodes and U the potential applied to the electrodes across a resistance R, and are obtained directly from 2 indicating electrodes without the need for a reference electrode.The advantage of these relationships over the classic I= f(E) curves, where E is the potential of the indicating electrode with respect to a reference electrode, is to facilitate the prediction of the titration curves as a function of the resistance R and the applied voltage U. The use of these relationships has shown that a fixed applied voltage U of 3 V and a fixed series resistance R of 0.5 megohm are the most suitable for a differential polarovoltmeter for semi-automatic titrations.A symbolic notation is described which indicates the origin of the observed variations in potential. This notation permits a simple interpretation of polarovoltric curves and the rational use of unsymmetrical electrode arrangements.     

A simple approach for the synthesis of new pyrimidinyl α-amino acids

A simple synthetic method for the preparation of optically active pyrimidinyl α-amino acids is presented. A nucleophilic ipso-substitution reaction between 2-(benzylsulfonyl)-4-isopropoxypyrimidines and a nucleophilic side chain of several protected natural α-amino acids is investigated to obtain new pyrimidin-2-yl α-amino acids. A detailed optimisation study of this reaction is discussed. Moreover, the selective O-alkylation of 2-(benzylsulfanyl)-4(3H)pyrimidinones with a hydroxylic side chain of some natural α-amino acids under Mitsunobu conditions is studied as a method to prepare new pyrimidin-4-yl α-aminoesters.     

The drag of the row of parallel chains of spherical particles in the Stokes flow

The drag of thin-layered porous deposit consisting of dendrites of identical spherical particles with respect to the flow of viscous incompressible liquid is calculated. The deposit is approximated by a model system, a row of parallel chains of particles oriented perpendicular to a flow direction. The expression is derived for the dimensionless drag force acting on the unit chain length as a function of the ratio of a particle radius to a half-distance between chain axes, a/h. It is shown that, at a/h < 0.5, the hydrodynamic equivalent of the chains is the smooth cylinder whose radius is 1.16 times smaller than the particle radius that agrees with the experiment. It is also shown that, at a/h = 1, the drag force of a particle contacting with four adjacent particles in the layer with square packing is equal to F = 44F _St, where F _St is the Stokes drag force of a spherical particle. The pressure drop in this single layer is by 3.5% higher than in the layer of spherical particles with cubic packing. At a/h = 2/√3, drag force F of the particle contacting with six particles in a single layer with hexagonal packing is equal to 340F _St.     

Two-photon ionization of an inner shell electron of the Cl atom

We have calculated, using second order perturbation theory, the two photon ionization cross section of a K-shell electron of chlorine forE=1.6 keV incident photons. Two classes of intermediate states must be considered, those in which a 1s electron moves to an emptyp-orbital, and those in which an electron from an occupiedp-orbital moves into the continuum. The first class of intermediate states is followed by the ejection of ap-electron into the continuum. The second class of intermediate states is followed by the transfer of a 1s electron into an emptyp-state. The largest contribution comes from 3p →d-continuum followed by 1s → 3p transition. Our result is σ⁽²⁾/I=2.06×10⁴¹ cm⁴/W where σ⁽²⁾ is the two photon ionization cross-section andI is the light intensity.     

Vertical excitation as a transient phenomenon

For a particular model with two electronic states, each with two vibrations, the dipole correlation function governing electronic absorption is e ^?iωOt cosγt with spectrum ω ₀±γ. The function starts as e ^?iωOt (γ?ω ₀), with Fourier transform peaking around ω ₀ instead of ω ₀±γ, and this is associated with vertical excitation. After a time t～2/γ the spectrum goes over into the normal one. As a generalization, a procedure is outlined for characterizing the state reached first after interaction with light is initiated. Finally it is suggested that one can understand aspects of internal conversion by analogy with the case of vertical excitation.     

A copper-catalyzed domino radical cyclization route to benzospiro-indolizidinepyrrolidinones

In this Letter the synthesis of benzospiro-indolizidinepyrrolidinones is described by a domino atom transfer radical cyclization reaction using a copper catalyst. The structure of one of the products was established by single crystal X-ray diffraction. The investigated precursors, bearing a homo allyl substituent on the N-indole, result in a 5-exo-trig, followed by a 6-endo-trig cyclization. When the N-indole is substituted with an allyl group, only the spiro-cyclization occurs.     

A master equation theory of excitonic annihilation phenomena for finite latices of low dimensionality

A master equation is written for the equation of motion for the vector p(t), in which the nth component corresponds to the probability of observing n excitons on a lattice with L sites. The dependence of the properties of p(t) on the magnitude of L, the intensity of excitation, the lattice dimensionality, and the magnitude of the biexcitonic annihilation rate is discussed. The dependence of the biexcitonic annihilation rate on the exciton density is discussed in the context of a simple simulation of exciton annihilation. The applicability of these ideas to excitonic annihilation in polymers is discussed.     

A new, improved synthesis of the trisaccharide repeating unit of the O-antigen from Xanthomonas campestris pv. campestris 8004

Recent studies have revealed that lipid-A and core fragments of the lipopolysaccharide from Xanthomonas campestris pv. campestris 8004 (Xcc), a phytopathogenic Gram-negative bacterium, are able to elicit plant immunity with two independent mechanisms. To date, nothing is known about the effect of the O-antigen portion. Since its separation from the core region by selective chemical degradation is very difficult, the chemical synthesis of related oligosaccharides is strictly necessary. In this paper a new, improved synthesis of the O-antigen repeating unit is presented. The main improvements in the synthesis are: (1) a shorter, high-yielding preparation of an efficient glycosyl donor of the rare sugar 3-acetamido-3,6-dideoxy-d-galactopyranose (3-acetamido-d-fucose, d-Fucp3NAc); (2) a new protecting group pattern, which is demonstrated to open a path to the future synthesis of higher oligomers.     

meta-Substituted triphenylamines as new dyes displaying exceptionally large Stokes shifts

A straightforward synthesis of fluorescent tris-meta-substituted triphenylamines (m-TPAs) is presented. These new fluorophores display a unique feature that is a remarkably high Stokes shift up to 250 nm, as compared to their para counterparts. Although the meta substitution is made at the expense of the quantum yield, the latter is maintained at an appreciable level (5%) making the m-TPAs a new class of fluorophores adaptable to a large range of applications from biology to materials science.     

Chemical-Genetic Interactions of Bacopa monnieri Constituents in Cells Deficient for the DNA Repair Endonuclease RAD1 Appear Linked to Vacuolar Disruption

Colorectal cancer is a common cancer worldwide and reduced expression of the DNA repair endonuclease XPF (xeroderma pigmentosum complementation group F) is associated with colorectal cancer. Bacopa monnieri extracts were previously found to exhibit chemical-genetic synthetic lethal effects in a Saccharomyces cerevisiae model of colorectal cancer lacking Rad1p, a structural and functional homologue of human XPF. However, the mechanisms for B. monnieri extracts to limit proliferation and promote an apoptosis-like event in RAD1 deleted yeast was not elucidated. Our current analysis has revealed that B. monnieri extracts have the capacity to promote mutations in rad1∆ cells. In addition, the effects of B. monnieri extracts on rad1∆ yeast is linked to disruption of the vacuole, similar to the mammalian lysosome. The absence of RAD1 in yeast sensitizes cells to the effects of vacuole disruption and the release of proteases. The combined effect of increased DNA mutations and release of vacuolar contents appears to induce an apoptosis-like event that is dependent on the meta-caspase Yca1p. The toxicity of B. monnieri extracts is linked to sterol content, suggesting saponins may be involved in limiting the proliferation of yeast cells. Analysis of major constituents from B. monnieri identified a chemical-genetic interaction between bacopasaponin C and rad1∆ yeast. Bacopasaponin C may have potential as a drug candidate or serve as a model for the development of analogs for the treatment of colorectal cancer.